where the map \(h\)  is a degree 16 isogeny sending a degree 0 line bundle \(F\)  to the point \(\sum c_2(i_{\textup {red}*}(F^{\otimes 2} \otimes \mathcal {I})) \in J\)  and \(i_{\textup {red}} \colon C_{\textup {red}}\rightarrow J\)  can be identified with the Albanese morphism. We conclude that \(g^{-1}(0)\)  is connected since the pullback of a connected étale cover of the Albanese variety by the Albanese map is connected (cf. [1]}). For a fixed line bundle \(F\)  in \(g ^{-1}(0)\) , the argument in [2]} implies that the possible extensions are parameterized by \(\mathbb {P}(\textup {Ext}^1_C(F,K)) \setminus \mathbb {P}(\textup {Ext}^1_{C_{\textup {red}}}(F,K)) \simeq \mathbb {C}^2\) . It follows that \(N_C^{II}\) , with its reduced, induced structure, is isomorphic to a \(\mathbb {C}^2\) -bundle over \(g^{-1}(0)\) .

